1. Field of the Invention
This invention relates to a photoelectric angle transducer employing a polarizer disc and more particularly to an angle transducer arranged to produce a sine wave output which varies in proportion to the angle to be measured.
2. Description of the Prior Art
In a control system for controlling the rotation angle of the arm of a robot, the table of a machine tool or the like, an angle transducer such as a rotary encoder, a resolver, etc. is used for detecting a feedback signal. Among these angle transducers, the resolver has a high resolution despite a simple structure thereof, and moreover enables one to obtain angle information at every period of the carrier wave thereof. The resolver has first and second coils which are wound around the poles of a stator arranged perpendicularly crossing two directions. The third coil is wound around a rotor which rotates within the resolver. Carrier waves Va and Vb which have a 90 degree phase difference relative to each other are supplied to the first and second coils. The carrier waves Va and Vb can be expressed as follows: EQU Va=V2 sin .omega.t EQU Vb=V2 cos .omega.t (1)
wherein V2 represents the amplitude of the carrier wave, and .omega. the angular velocity of the carrier wave.
These poles are thus arranged to radiate magnetic flux corresponding to the carrier waves. Therefore, when the rotor is allowed to rotate by coupling it with a shaft to be measured, the ratio of a portion of each radiated magnetic flux that interlinks with the rotor varies with the angle of rotation .theta.. As a result, at the third coil, there is induced a phase signal Vc which changes the phase thereof accordingly as the rotation angle .theta. changes and which can be expressed as follows: ##EQU1## wherein K2 and K3 represent coefficients of proportion.
However, since the resolver is using the above stated means for generating an electromagnetic signal, it necessitates use of a coil and a rotary transformer in order to receive a signal from the coil. This restricts any possible reduction in size. Further, the rotor has a greater moment of inertia than that of a rotary encoder. In addition to these problems, in order to obtain the desired magnetic flux distribution, the shape and allocation of the coil must be very precisely determined during the manufacturing process. This results in an increase in the cost thereof.
These shortcomings of the resolver stem from the use of the electromagnetic signal generating means. Therefore, it is conceivable to solve these problems by use of photo-electric signal generating means in place of the electromagnetic signal generating means. An example of known angle transducers based on this concept has been disclosed, for example, in U.S. Pat. No. 3,306,159. In that case, the rotor is arranged to be a polarizer disc. This polarizer rotor is opposed to first -fourth polarizer plates. The transmission axes of these polarizer plates are arranged on the tilt differing 45 degrees from each other. The first - fourth polarizer plates and the polarizer rotor are interposed between light sources and first -fourth photoelectric conversion elements which are opposed to the light sources, respectively. The output signals of these first - fourth photo-electric conversion elements are arranged to modulate the amplitude of carrier waves mutually deviating by 90 degrees in phase. The four modulated signals thus obtained are arranged in preparation for addition. The operation of the angle transducer which is arranged in this manner is as described by the formulas below. Assuming that the light quantity of the light source is Io and the intersectional angle of the transmission axes of the polarizer rotor and the polarizer plate is .alpha., the quantity of light I.sub. .alpha. reaching the photo-electric conversion element can be expressed by the law of Malus as follows: ##EQU2## wherein H.sub.0 : transmission factor of parallel position (.alpha.=0); H.sub.90 : transmission factor of orthogonal position (.alpha.=90); K.sub.4 =(H.sub.0 -H.sub.90)/2; K.sub.5 =(H.sub.0 +H.sub.90)/2 and .beta.: transmission factor at intersectional angle .alpha..
Therefore, assuming that the rotation angle of the polarizer rotor is .theta., the transmission factors .beta.a -.beta.d of the first - fourth polarizer plates which have their transmission axes mutually deviating by 45 degrees can be expressed as follows: EQU .beta.a=K.sub.4 cos2.theta.+K.sub.5 EQU .beta.b=K.sub.4 cos2(.theta.+45.degree.)+K.sub.5 =-K.sub.4 sin2.theta.+K.sub.5 EQU .beta.c=K.sub.4 cos2(.theta.+90.degree.)+K.sub.5 =-K.sub.4 cos2.theta.+K.sub.5 EQU .beta.d=K.sub.4 cos2(.theta.+135.degree.)+K.sub.5 =K.sub.4 sin2.theta.+K.sub.5 ( 4)
As a result, voltage signals fa'-fd' generated at the photo-electric conversion elements result in a correspondence with the transmission factors of formula (4) above. Then, with the coefficients of proportion K.sub.4 and K.sub.5 replaced with predetermined coefficients K.sub.6 and K.sub.7, the voltage signals can be expressed as follows: EQU fa'=K.sub.6 cos2.theta.+K.sub.7 EQU fb'=-K.sub.6 sin2.theta.+K.sub.7 EQU fc'=-K.sub.6 cos2.theta.+K.sub.7 EQU fd'=K.sub.6 sin2.theta.+K.sub.7 ( 5)
Next, the amplitudes of the carrier waves which have their phases mutually deviating by 90 degrees are modulated by these voltage signals to obtain modulated signals ja'-jd', which can be expressed as follows: EQU ja'=K.sub.6 cos2.theta.sin.omega.t+K.sub.7 sin.omega.t EQU jb'=-K.sub.6 sin2.theta.cos.omega.t+K.sub.7 cos.omega.t EQU jc'=K.sub.6 cos2.theta.sin.omega.t-K.sub.7 sin.omega.t EQU jd'=-K.sub.6 sin2.theta.cos.omega.t-K.sub.7 cos.omega.t (6)
The modulated signals ja'-jd' are added together. As a result of this addition, a phase signal P of a sine wave which has its phase in variation with the double angle of the rotation angle .theta., is obtained. The phase signal P can be expressed as follows: ##EQU3##
However, the angle transducer of the prior art inevitably has a somewhat complex structure as it necessitates use of a light source, four polarizer plates, four photo-electric conversion elements and a polarizer rotor. To solve this problem, U.S. Pat. No. 3,932,039 has disclosed an angle transducer in which the number of the polarizer plates and that of the photo-electric conversion elements are respectively reduced to two.
In this angle transducer, two of the voltage signals shown in formula (5) above, say, the signals fa' and fb' are taken out. The ratio of the two voltage signal fa'/fb' is compared with that of reference waves Va and Vb, which are obtained from the above stated carrier waves and can be expressed as follows: EQU Va=Etcos.omega.t+Kt EQU Vb=Etcos(.omega.t+90.degree.)+Kt=-Etsin.omega.t+Kt (8)
wherein Et and Kt represent constants.
When the ratio fa'/fb' comes to coincide with the ratio Va/Vb, the angle transducer produces a pulse. In other words, a coincidence pulse is arranged to be produced when the following condition is satisfied: ##EQU4##
Thus, the pulse is produced every time a condition of 2.theta.=.omega.t, i.e. time t=2.theta./.omega., is satisfied. Accordingly, the time width of a synchronizing pulse generated for every period of the above stated reference wave Va or Vb and the above stated coincidence pulse, varies with the double angle of the rotation angle .theta.. In the case of the transducer, the phase signal is thus obtained in the form of a square wave the time width of which varies according to the double angle of the rotation angle .theta.. The transducer is capable of solving the problems of the resolver with simplified structural arrangement for reduction in size. However, it is a shortcoming of the angle transducer that, unlike the above stated resolver and the angle transducer of U.S. Pat. No. 3,306,159, the phase signal obtained by the transducer is either in the form of a pulse train or a square wave. This presents a problem, for example, in a case where the angle transducer is to be used for detection of the feedback signal of a synchronous motor control system of the permanent magnet type. In such a case, if the phase signal is of a sine wave form, phase difference signals can be prepared to represent phase differences between the phase signal and carrier waves mutually deviating in phase by 90 degrees. Then, the magnitude of each of these phase difference signals comes to correspond to the phase of the phase signal as it is. In other words, they come to correspond to the sine function of double angle of the rotation angle .theta. and to sine functions deviating therefrom by 90 degrees in phase. Therefore, with the phase difference signals converted into three phase signals, motor driving sine wave signals of three phases can be obtained, whereas, in the event of the phase signal of a square wave form, if phase difference signals representing phase differences between the phase signal and the carrier waves mutually deviating by 90 degrees in phase are prepared, the magnitude of each phase difference signal comes to correspond to the phase of the phase signal. In other words, it comes to correspond to a triangular wave of the rotation angle .theta. and a triangular wave deviating therefrom by 90 degrees in phase. Therefore, this necessitates the use of an additional circuit for converting the triangular wave into a sine wave. In accordance with the arrangement of this transducer, therefore, it is inevitable to have a more complex circuit and a response delay resulting from the use of the complex circuit.